<< Chapter < Page
  Digital signal processing - dsp     Page 11 / 24
Chapter >> Page >

As mentioned earlier, the DFT algorithm is much more flexible while the FFT algorithm is much faster, particularly for large data lengths.

Peaks merge at the folding frequency

In addition to illustrating these fundamental aspects of the DFT algorithm, this example also illustrates how the mirror image peaks on either side of thefolding frequency merge into a single larger peak as the data frequency approaches the folding frequency.

The input parameters

The input parameters are shown in Figure 10 . Note in particular the values for the following parameters:

  • Data length: 200
  • Sample for zero time: 0
  • Lower frequency bound: 0.4
  • Upper frequency bound: 0.6
Figure 10. The input parameters.
Data length: 200 Sample for zero time: 0Lower frequency bound: 0.4 Upper frequency bound: 0.6Number spectra: 5 Frequencies0.492 0.4940.496 0.4980.5 Amplitudes90.0 90.090.0 90.090.0

A different data length

As you can see, the data length for this experiment is different from the data length of 400 used earlier. In addition, neither data length is a power oftwo.

Computational frequency bounds

As you can also see, the lower and upper frequency bounds are not 0.0 and 1.0 as in the earlier cases. In this case, the frequency bounds describe a muchnarrower range centered on the folding frequency.

Frequencies are close to the folding frequency

Finally, the frequencies of each of the five sinusoids specified in Figure 10 is progressively closer to the folding frequency with the frequency of the fifthsinusoid being equal to the folding frequency.

The spectral analysis output

The output from the spectral analysis for each of the five sinusoids is shown in Figure 11 . (Another interesting view of the same results is shown later in Figure 14 .)

Figure 11. Spectral analysis of five sinusoids.
missing image

Peaks are symmetrical about the folding frequency

The spectral peaks shown in Figure 11 are symmetrical about the folding frequency, which in turn is centered horizontally in each of the graphs. As youalready know, the peaks are always symmetrical about the folding frequency due to the frequency folding at that frequency.

The folding frequency is centered horizontally due to the way that I defined the lower and upper frequency bounds, and the way that I adjusted the plottingparameters.

Peaks are well defined and wider than before

The peaks are well defined because I computed the spectral energy at 200 points across the specified frequency range from 0.4 to 0.6. Thus, the frequencybins at which I computed spectral energy were much narrower than before.

The peaks are wider because I displayed a much smaller slice of the entire frequency spectrum in the same physical screen space.

Peaks merge at the folding frequency

As the frequency of each sinusoid approaches the folding frequency, the two mirror-image peaks corresponding to that sinusoid merge into a single peak withtwice the height at the folding frequency. This agrees with what you saw in Figure 9 , but on a much more detailed basis.

It would be difficult to perform this experiment using an FFT algorithm because of the inherent limitations built into the algorithm. The FFT algorithmsacrifices flexibility for speed.

Questions & Answers

the art of managing the production, distribution and consumption.
Satangthem Reply
what is economics
Khawar Reply
okk
damfash
marginal utility is the additional satisfaction one derives from consuming additional unit of a good or service.
Fred
It's the allocation of scarce resources.
Fred
marginal utility please?
Dishan
marginal utility is the additional satisfaction one derives from consuming additional unit of a good or service.
Fred
I know the definition, but I don't understand its meaning.
Dishan
what is the must definition of economic please?
Nurudeen
demand lfs
Alpha
Economics is derived from the word Oikonomia which means management of household things. Thus, Economics is a study of household things with the constrains of allocating scare resources.
Dishan
what is Open Market Operation
Adu Reply
dominating middlemen men activities circumstances
Christy Reply
what Equilibrium price
Adji Reply
what is gap
mirwais
who is good with the indifference curve
Dexter
What is diseconomic
Alixe Reply
what are the types of goods
WARIDI
how can price determination be the central problem of micro economics
simon Reply
marginal cost formula
Nandu Reply
you should differentiate the total cost function in order to get marginal cost function then you can get marginal cost from it
boniphace
What about total cost
Foday
ok
Foday
how can price determination be the central problem if micro economics
simon
formula of cross elasticity of demand
Theresia Reply
what is ceteris paribus
Priyanka Reply
what is ceteris parabus
Priyanka
Ceteris paribus - Literally, "other things being equal"; usually used in economics to indicate that all variables except the ones specified are assumed not to change.
Abdullah
What is broker
scor
land is natural resources that is made by nature
scor
What is broker
scor
what is land
kafui
What is broker
scor
land is natural resources that is made by nature
scor
whats poppina nigga turn it up for a minute get it
amarsyaheed Reply
what is this?
Philo
am from nigeria@ pilo
Frank
am from nigeria@ pilo
Frank
so
owusu
what is production possibility frontier
owusu
it's a summary of opportunity cost depicted on a curve.
okhiria
please help me solve this question with the aid of appropriate diagrams explain how each of the following changes will affect the market price and quantity of bread 1. A
Manuela Reply
please l need past question about economics
Prosper Reply
ok let me know some of the questions please.
Effah
ok am not wit some if den nw buh by tommorow I shall get Dem
adepojurafiu
Hi guys can I get Adam Smith's WEALTH OF NATIONS fo sale?
Ukpen
hello I'm Babaisa alhaji Mustapha. I'm studying Economics in the university of Maiduguri
Babaisa
okay
Humaira
my name is faisal Yahaya. i studied economics at Kaduna state university before proceeding to West African union university benin republic for masters
Faisal
Hi guys..I am from Bangladesh..
Mannan
Wat d meaning of management
igwe Reply
disaster management cycle
Gogul Reply
cooperate social responsibility
igwe
Fedric Wilson Taylor also define management as the act of knowing what to do and seeing that it is done in the best and cheapest way
OLANIYI
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Beverly Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing - dsp' conversation and receive update notifications?

Ask